8.4 Matrices

Matrices are defined by a gsl_matrix structure which describes a
generalized slice of a block. Like a vector it represents a set of
elements in an area of memory, but uses two indices instead of one.

The gsl_matrix structure contains six components, the two
dimensions of the matrix, a physical dimension, a pointer to the memory
where the elements of the matrix are stored, data, a pointer to
the block owned by the matrix block, if any, and an ownership
flag, owner. The physical dimension determines the memory layout
and can differ from the matrix dimension to allow the use of
submatrices. The gsl_matrix structure is very simple and looks
like this,

Matrices are stored in row-major order, meaning that each row of
elements forms a contiguous block in memory. This is the standard
“C-language ordering” of two-dimensional arrays. Note that FORTRAN
stores arrays in column-major order. The number of rows is size1.
The range of valid row indices runs from 0 to size1-1. Similarly
size2 is the number of columns. The range of valid column indices
runs from 0 to size2-1. The physical row dimension tda, or
trailing dimension, specifies the size of a row of the matrix as
laid out in memory.

For example, in the following matrix size1 is 3, size2 is 4,
and tda is 8. The physical memory layout of the matrix begins in
the top left hand-corner and proceeds from left to right along each row
in turn.

Each unused memory location is represented by “XX”. The
pointer data gives the location of the first element of the matrix
in memory. The pointer block stores the location of the memory
block in which the elements of the matrix are located (if any). If the
matrix owns this block then the owner field is set to one and the
block will be deallocated when the matrix is freed. If the matrix is
only a slice of a block owned by another object then the owner field is
zero and any underlying block will not be freed.

The functions for allocating and accessing matrices are defined in
gsl_matrix.h